Common Fixed-Point Theorems via Notion of Pairwise Semi-Compatible Mappings and Occasionally Weakly Compatible Mappings (OWC) for Six Self-Mappings in Fuzzy Metric Spaces

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Department of Mathematics, Aurora's Technological and Management Academy, Hyderabad, Telangana, India.
Periodicity:January - June'2023
DOI : https://doi.org/10.26634/jmat.12.1.19308

Abstract

The notion of occasionally weakly compatible mappings, and Semi compatible mappings in fuzzy metric space is discussed in this research. The paper investigates the Common fixed-point theorems in fuzzy metric spaces. By taking the property of commutativity of pair mappings, the pairwise semi-compatible mappings and occasionally weakly compatible mappings, satisfying constructive type condition for six self-mappings the common fixed-point theorems in fuzzy metric spaces were proved. The result improves and generalizes other similar results in the literature.

Keywords

Fuzzy Metric Space (FM-Space), Fixed Point, Property E.A., Compatible Mapping.

How to Cite this Article?

Singh, T. R. (2023). Common Fixed-Point Theorems via Notion of Pairwise Semi-Compatible Mappings and Occasionally Weakly Compatible Mappings (OWC) for Six Self-Mappings in Fuzzy Metric Spaces. i-manager’s Journal on Mathematics, 12(1), 29-36. https://doi.org/10.26634/jmat.12.1.19308

References

[1]. Abbas, M., Altun, I., & Gopal, D. (2009). Common fixed point Theorems for non compatible mappings in fuzzy metric spaces. Bulletin of Mathematical Analysis and Applications [Electronic only], 1(2), 47-56.
[3]. Al-Thagafi, M. A., & Shahzad, N. (2009). A note on occasionally weakly compatible maps. International Journal of Mathematical Analysis, 3(2), 55-58.
[4]. Cho, Y. J., Sharma, B. K., & Sahu, D. R. (1995). Semi-compatibility and fixed points. Mathematica Japonicae, 42(1), 91-98.
[5]. Gupta, V., Deep, R., & Tripathi, A. K. (2018). Some common fixed point theorems in fuzzy metric spaces and their applications. Boletim da Sociedade Paranaense de Matemática, 36(3), 141-153.
[6]. Jain, A., & Chaudhary, B. (2013). On common fixed point theorems for semi-compatible and occasionally weakly compatible mappings in Menger space. International Journal of Research and Reviews in Applied Sciences, 14(3), 662- 670.
[7]. Jungck, G. (1986). Compatible mappings and common fixed points. International Journal of Mathematics and Mathematical Sciences, 9(4), 771-779.
[8]. Kaleva, O., & Seikkala, S. (1984). On fuzzy metric spaces. Fuzzy Sets and Systems, 12(3), 215-229. https://doi.org/10. 1016/0165-0114(84)90069-1
[9]. Kramosil, I., & Michálek, J. (1975). Fuzzy metrics and statistical metric spaces. Kybernetika, 11(5), 336-344.
[10]. Mishra, S. N., Sharma, N., & Singh, S. L. (1994). Common fixed points of maps on fuzzy metric spaces. International Journal of Mathematics and Mathematical Sciences, 17(2), 253-258.
[11]. Pant, V., & Pant, R. P. (2007). Fixed points in fuzzy metric space for noncompatible maps. Soochow Journal of Mathematics, 33(4), 647-655.
[12]. Sessa, S. (1982). On a weak commutativity condition of mappings in fixed point considerations. Publications de l'Institut Mathématique, 32(46), 149-153.
[15]. Singh, B., & Jain, S. (2005b). Weak compatibility and fixed point theorems in fuzzy metric spaces. Ganita, 56(2), 167-176.
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